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Mat. Zametki, 2013, Volume 93, Issue 3, Pages 442–447 (Mi mz10163)  

This article is cited in 2 scientific papers (total in 2 papers)

Duality Properties for $\mathrm{b}$-$\mathrm{AM}$-Compact Operators on Banach Lattices

Na Cheng, Zi-Li Chen, Guang-Gui Chen

Xihua University, Sichuan

Abstract: We obtain some necessary and some sufficient conditions on Banach lattices $E$ and $F$ such that (i) if $T\colon E\to F$ is a $\mathrm{b}$-$\mathrm{AM}$-compact operator, then $T'\colon F'\to E'$ is also $\mathrm{b}$-$\mathrm{AM}$-compact operator and (ii) if $T'\colon F'\to E'$ is $\mathrm{b}$-$\mathrm{AM}$-compact operator, then $T\colon E\to F$ is also $\mathrm{b}$-$\mathrm{AM}$-compact operator.

Keywords: Banach lattice, $\mathrm{b}$-$\mathrm{AM}$-compact operator, discrete space.

DOI: https://doi.org/10.4213/mzm10163

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English version:
Mathematical Notes, 2013, 93:3, 465–469

Bibliographic databases:

UDC: 517.983
Received: 20.02.2011

Citation: Na Cheng, Zi-Li Chen, Guang-Gui Chen, “Duality Properties for $\mathrm{b}$-$\mathrm{AM}$-Compact Operators on Banach Lattices”, Mat. Zametki, 93:3 (2013), 442–447; Math. Notes, 93:3 (2013), 465–469

Citation in format AMSBIB
\Bibitem{Na Zi-Gua13}
\by Na Cheng, Zi-Li Chen, Guang-Gui Chen
\paper Duality Properties for $\mathrm{b}$-$\mathrm{AM}$-Compact Operators on Banach Lattices
\jour Mat. Zametki
\yr 2013
\vol 93
\issue 3
\pages 442--447
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\crossref{https://doi.org/10.4213/mzm10163}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3205992}
\elib{http://elibrary.ru/item.asp?id=20731701}
\transl
\jour Math. Notes
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\vol 93
\issue 3
\pages 465--469
\crossref{https://doi.org/10.1134/S0001434613030139}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. Cheng, “Dedekind $\sigma$-complete vector lattice of $\mathrm{b}$-$\mathrm{AM}$-compact operators”, Quaest. Math., 40:3 (2017), 313–318  crossref  mathscinet  isi
    2. N. Cheng, “Some results on b-AM-compact operators”, Quaest. Math., 41:6 (2018), 839–845  crossref  mathscinet  zmath  isi  scopus
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